Physics constrained nonlinear regression models for time series

Nonlinearity

Volumn 26, Issue 1, 2013, Pages 201-217

  Majda, Andrew J ^a   Harlim, John ^b  

^a NEW YORK UNIVERSITY   (United States)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84870475304     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/26/1/201     Document Type: Article

References (39)

1. Horenko I 2010 Finite element approach to clustering of multidimensional time series SIAM J. Sci. Comput. 32 68-83
2. Horenko I 2010 On the identification of nonstationary factor models and their application to atmospheric data analysis J. Atmos. Sci. 67 1559-74
3. Crommelin D and Vanden-Eijnden E 2008 Subgrid-scale parameterization with conditional Markov chains J. Atmos. Sci. 65 2661-75
4. Priestly M B 1988 Non-linear and Non-Stationary Time Series Analysis (London: Academic)
5. Tong H 1990 Nonlinear Time Series: A Dynamical Systems Approach (Oxford: Oxford University Press)
6. Cressie N and Wikle C K 2011 Statistics for Spatio-Temporal Data (Hoboken, NJ: Wiley)
7. Pavliotis G A and Stuart A M 2007 Parameter estimation for multiscale diffusions J. Stat. Phys. 127 741-81
8. Azencott R, Beri A and Timofeyev I 2010 Adaptive sub-sampling for parametric estimation of gaussian diffusions J. Stat. Phys. 139 1066-89
9. Majda A J, Franzke C L, Fischer A and Crommelin D T 2006 Distinct metastable atmospheric regimes despite nearly gaussian statistics: a paradigm model Proc. Natl Acad. Sci. 103 8309-14 (Pubitemid 43838451)
10. Franzke C, Horenko I, Majda A J and Klein R 2009 Systematic metastable atmospheric regime identification in an AGCM J. Atmos. Sci. 66 1997-2012
11. Kravtsov S, Kondrashov D and Ghil M 2005 Multilevel regression modeling of nonlinear processes: derivation and applications to climatic variability J. Clim. 18 4404-24 (Pubitemid 41805480)
12. Kondrashov D, Kravtsov S, Robertson A W and Ghil M 2005 A hierarchy of data-based enso models J. Clim. 18 4425-44 (Pubitemid 41805481)
13. Kondrashov D, Kravtsov S and Ghil M 2006 Empirical mode reduction in a model of extratropical low-frequency variability J. Atmos. Sci. 63 1859-77 (Pubitemid 44184030)
14. Wikle C and Hooten M 2010 A general science-based framework for dynamical spatio-temporal models TEST 19 417-51
15. Majda A J and Yuan Y 2012 Fundamental limitations of ad hoc linear and quadratic multi-level regression models for physical systems Discrete Conti. Dyn. Syst. B 17 1333-63
16. Majda A J, Timofeyev I and Vanden-Eijnden E 1999 Models for stochastic climate prediction Proc. Natl Acad. Sci. 96 15687-91 (Pubitemid 30019700)
17. Majda A J, Timofeyev I and Vanden-Eijnden E 2001 A mathematical framework for stochastic climate models Commun. Pure Appl. Math. 54 891-974
18. Majda A J, Franzke C and Khouider B 2008 An applied mathematics perspective on stochastic modelling for climate Phil. Trans. A Math. Phys. Eng. Sci. 366 2429-55
19. Majda A J, Abramov R V and Grote M J 2005 Information Theory and Stochastics for Multiscale Nonlinear Systems (CRM Monograph Series vol 25) (Providence, RI: American Mathematical Society)
20. Majda A J, Franzke C and Crommelin D 2009 Normal forms for reduced stochastic climate models Proc. Natl Acad. Sci. 106 3649-53
21. Franzke C, Majda A J and Vanden-Eijnden E 2005 Low-order stochastic mode reduction for a realistic barotropic model climate J. Atmos. Sci. 62 1722-45 (Pubitemid 41135963)
22. Yuan Y and Majda A J 2011 Invariant measures and asymptotic gaussian bounds for normal forms of stochastic climate model Chin. Ann. Math. B 32 343-68
23. Strounine K, Kravtsov S, Kondrashov D and Ghil M 2010 Reduced models of atmospheric low-frequency variability: parameter estimation and comparative performance Physica D 239 145-66
24. Majda A J and Timofeyev I 2002 Statistical mechanics for truncations of the Burgers-Hopf equation: a model for intrinsic behavior with scaling Milan J. Math. 70 39-96
25. Majda A J, Timofeyev I and Vanden-Eijnden E 2006 Stochastic models for selected slow variables in large deterministic systems Nonlinearity 19 769-94 (Pubitemid 43432186)
26. Kwasniok F 2007 Reduced atmospheric models using dynamically motivated basis functions J. Atmos. Sci. 64 3452-74 (Pubitemid 350041853)
27. Mattingly J C, Stuart A M and Higham D J 2002 Ergodicity for SDES and approximations: locally Lipschitz vector fields and degenerate noise Stoch. Process. Appl. 101 185-232
28. Macki J and Strauss A 1981 Introduction to Optimal Control Theory (Undergraduate Texts in Mathematics) (Berlin: Springer)
29. Majda A J, Timofeyev I and Vanden-Eijnden E 2002 A priori tests of a stochastic mode reduction strategy Physica D 170 206-52
30. Hormander L 1985 The analysis of linear partial differential operators: III. Pseudo-differential operators (Grundlehren der Mathematischen Wissenschaften in Einzeldarstellungen vol 3) (Berlin: Springer)
31. Hirsch M and Smale S 1974 Differential Equations, Dynamical Systems, and Linear Algebra (New York: Academic)
32. Kunita H 1978 Supports of diffusion processes and controllability problems Proc. Int. Symp. Stochastic Differential Equations (Kyoto University, Japan,) (New York: Wiley) pp 163-85
33. Friedland B 1969 Treatment of bias in recursive filtering IEEE Trans. Automat. Contr. AC-14 359-67
34. Belanger P R 1974 Estimation of noise covariance matrices for a linear time-varying stochastic process Automatica 10 267-75
35. Anderson B D and Moore J B 1979 Optimal Filtering (Englewood Cliffs, NJ: Prentice-Hall)
36. Chui C and Chen G 1999 Kalman Filtering: with Real-Time Applications (New York: Springer)
37. Branicki M, Gershgorin B and Majda A J 2012 Filtering skill for turbulent signals for a suite of nonlinear and linear extended Kalman filters J. Comput. Phys. 231 1462-98
38. Baek S-J, Hunt B R, Kalnay E, Ott E and Szunyogh I 2006 Local ensemble Kalman filtering in the presence of model bias Tellus A 58 293-306
39. Kang E L, Harlim J and Majda A J 2013 Regression models with memory for the linear response of turbulent dynamical systems Commun. Math. Sci. 11 481-98